In the first part of this study, we present results of fully self-consistent Hartree-Fock based random phase approximation calculations of the strength functions S(E) and centroid energies ECEN of isoscalar (T = 0) and isovector (T = 1) giant resonances of multipolarities L = 0 - 3 in 40Ca, 48Ca, and 208Pb using a wide range of 34 commonly employed Skyrme type nucleon-nucleon effective interactions. We determined the sensitivities of ECEN and of the isotopic differences ECEN(48Ca) - ECEN(40Ca) to physical quantities, such as nuclear matter incompressibility coefficient, symmetry energy density and effective mass, associated with the Skyrme interactions and compare the results with the available experimental data.
In the second part of this study, we present a novel method, using the single particle Schrodinger equation, to determine the central potential directly from the single particle matter density and its first and second derivatives. As an example, we consider the experimental data for the charge density difference between the isotones 206Pb - 205Tl, deduced by analysis of elastic electron scattering measurements which corresponds to the shell model 3s1/2 proton orbit, and determine the corresponding single particle potential (mean-field). We also present results of least-square fits to parametrized single particle potentials. The 3s1/2 wave functions of the determined potentials reproduce fairly well the experimental data within the quoted errors. More accurate experimental data, with uncertainty smaller by a factor of two or more, may answer the question how well can the data be reproduced by a calculated 3s1/2 wave function.
- Shlomo, Shalom Senior Scientist